The 16th term of an AP is three times the 5th term. If the 12th term is 20 more than the 7th term, find the first term and the common difference.

Answer 1

5 d = 20 ... d = 4

T5 + 11d = 3 T5 ... T5 = 22

T1 = T5 - 4d

Answer 2

a= 5, d=7

Answer 3

Tn=a +(n-1)d
T12 = 20+T7,
a +11d = 20 + a + 6d,
5 d = 20, d = 4.

T16 = 3T5,
a + (16 - 1)d = 3[a+(5-1)d],
a + (16 - 1)4 = 3[a+(5-1)4],
a+60 =3a+48,
3a-a = 60 - 48.
2a = 12
a= 6

a = 6, d = 4